CN110322062A - Short-Term Load Forecasting Method - Google Patents
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- G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
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- G06N20/10—Machine learning using kernel methods, e.g. support vector machines [SVM]
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Abstract
The present invention relates to power prediction fields, more specifically, it is related to a kind of Short-Term Load Forecasting Method, include: to obtain short-term electric load sample data from historical data to be analyzed for short-term electric load sample data using principal component analysis technology, obtains the principal component component data of short-term electric load；Supporting vector machine model is constructed, and training set is constructed according to principal component component data；Supporting vector machine model is trained with training set, obtains Short-term Load Forecasting；The following short-term electric load is predicted using the Short-term Load Forecasting.The present invention can carry out accurate, real-time, reliable prediction to future electrical energy load.
Description
Technical field
The present invention relates to power prediction fields, more specifically to a kind of Short-Term Load Forecasting Method.
Background technique
Load forecast is the important component of electricity market Energy Management System.Short-term electric load prediction is needle
To short term randomness and uncertain feature, under conditions of comprehensively considering weather condition, social factor, sufficiently research and
Using existing historical data, the mathematical model of a set of the features such as meeting historical data continuity, periodicity is established, it is higher meeting
In the sense that precision, the electric load of coming few hours, one day or several days is determined.
Therefore, load forecast is power system security, layout in the effective guarantee of economical operation and market environment
Operation plan, power supply plan, trading program basis.It is horizontal to improve Short Term load Forecasting Technique, is conducive to power system security
Stable operation advantageously reduces operation power cost, is conducive to coordinate power generation, transmission of electricity and electricity consumption relationship, promotes electric power enterprise effect
Benefit.In the trend of power generation and consumption market, to the accuracy of load prediction, real-time, reliability and intelligent
Demand is growing day by day, and electric system scale constantly expands, and electric power data resource sharply exponentially increases, and causes " dimension calamity
It is difficult ", seriously affect precision of prediction.Correspondingly, how key factor is excavated in mass data, reduce the complicated journey of prediction model
Degree improves the important subject that load forecast precision has become electric power enterprise.
Summary of the invention
The technical problem to be solved in the present invention is that in view of the drawbacks of the prior art, it is pre- to provide a kind of short-term electric load
Survey method can carry out accurate, real-time, reliable prediction to future electrical energy load.
The technical solution adopted by the present invention to solve the technical problems is: construction Short-Term Load Forecasting Method, comprising:
Short-term electric load sample data is obtained from historical data；
It is analyzed for short-term electric load sample data using principal component analysis technology, obtains short-term electric load
Principal component component data；
Supporting vector machine model is constructed, and training set is constructed according to principal component component data；
Supporting vector machine model is trained with training set, obtains Short-term Load Forecasting；
The following short-term electric load is predicted using the Short-term Load Forecasting.
It is described that short-term electric load sample data is obtained from historical data in above scheme, it specifically includes:
Historical load data is obtained from historical data；
By historical load data arrange for matrix size be m × k dimension sample matrix, the sample matrix be short term power
Load sample data.
It is described to be analyzed for short-term electric load sample data using principal component analysis technology in above scheme, it obtains
To the principal component component data of short-term electric load, specifically include:
Short-term electric load sample data is subjected to centralization, obtains average data collection；
Calculate the covariance matrix for removing average data collection；
Find out the characteristic value and corresponding feature vector of the covariance matrix；
The characteristic value of the covariance matrix is sorted from large to small, maximum n characteristic value is taken out, the n is at least
1；
By feature vector composition characteristic matrix corresponding to n characteristic value；
The constraint function of principal component component is constructed, and short-term electric load sample data is projected in eigenmatrix, is obtained
To the principal component component data of short-term electric load.
It is described that supporting vector machine model is trained with training set in above scheme, it is pre- to obtain short-term electric load
Model is surveyed, is specifically included:
By Wolfe dual theorem combination method of Lagrange multipliers, the original optimization problem of supporting vector machine model is turned
Turn to the primal-dual optimization problem of supporting vector machine model；
Kernel function is introduced, and is solved with primal-dual optimization problem of the training set to supporting vector machine model, is obtained short
Phase power load forecasting module.
In above scheme, the constraint function of the principal component component are as follows:
s.t.WTW=I (6)
In formula (6), W is the principal component component data of short-term electric load, and X is to remove average data collection.
In above scheme, the supporting vector machine model are as follows:
F (x)=ω × φ (xi)+b (8)
In formula (8), in formula, ω × φ (x) is the inner product of higher dimensional space vector ω and Nonlinear Mapping φ (x), ω's
Dimension is higher dimensional space dimension, and b ∈ R is amount of bias.
In above scheme, the original optimization problem of the supporting vector machine model are as follows:
The constraint condition of formula (9) are as follows:
For formula (9) into (10), C is penalty coefficient, and the data sample that training error is more than ε is punished more in the bigger expression of C
Greatly, ξ and ξ*For slack variable, ε is insensitive loss function, the expression formula of ε are as follows:
In formula (11), f (x) indicates that the regression estimates function of support vector machines, y indicate prediction output valve.
In above scheme, the primal-dual optimization problem of the supporting vector machine model are as follows:
The constraint condition of formula (12) are as follows:
Formula (12) is into (13), αiWithBe Lagrange multiplier andxiFor supporting vector, b is
Threshold value.
In above scheme, the kernel function are as follows:
In formula (15), x is the center of kernel function；σ2For the form parameter of kernel function.
In above scheme, the Short-term Load Forecasting are as follows:
In formula (16), f (x) indicates the regression estimates function of support vector machines.
The beneficial effects of the present invention are:
In the present invention, it applies to principal component analysis technology to analyze short-term electric load sample data, thus
The correlation and noise of data can be eliminated, the pivot comprising short-term electric load sample information is extracted, reduces the dimension of sample space
Number greatly simplifies calculating and saves space, to the arithmetic speed of supporting vector machine model training in step after raising.
Detailed description of the invention
Present invention will be further explained below with reference to the attached drawings and examples, in attached drawing:
Fig. 1 is flow diagram of the present invention.
Specific embodiment
For a clearer understanding of the technical characteristics, objects and effects of the present invention, now control attached drawing is described in detail
A specific embodiment of the invention.
As shown in Figure 1, in a kind of Short-Term Load Forecasting Method of the invention, comprising:
101, short-term electric load sample data is obtained from historical data；
102, it is analyzed for short-term electric load sample data using principal component analysis technology, it is negative to obtain short term power
The principal component component data of lotus；
103, supporting vector machine model is constructed, and training set is constructed according to principal component component data；
104, supporting vector machine model is trained with training set, obtains Short-term Load Forecasting；
105, the following short-term electric load is predicted using the Short-term Load Forecasting.
Further, described that short-term electric load sample data is obtained from historical data, it specifically includes:
Historical load data is obtained from historical data；
By historical load data arrange for matrix size be m × k dimension sample matrix, the sample matrix be short term power
Load sample data.
Further, described to be analyzed for short-term electric load sample data using principal component analysis technology, it obtains
To the principal component component data of short-term electric load, specifically include:
Short-term electric load sample data is subjected to centralization, obtains average data collection；
Calculate the covariance matrix for removing average data collection；
Find out the characteristic value and corresponding feature vector of the covariance matrix；
The characteristic value of the covariance matrix is sorted from large to small, maximum n characteristic value is taken out, the n is at least
1；
By feature vector composition characteristic matrix corresponding to n characteristic value；
The constraint function of principal component component is constructed, and short-term electric load sample data is projected in eigenmatrix, is obtained
To the principal component component data of short-term electric load.
Still further, described be trained supporting vector machine model with training set, it is pre- to obtain short-term electric load
Model is surveyed, is specifically included:
By Wolfe dual theorem combination method of Lagrange multipliers, the original optimization problem of supporting vector machine model is turned
Turn to the primal-dual optimization problem of supporting vector machine model；
Kernel function is introduced, and is solved with primal-dual optimization problem of the training set to supporting vector machine model, is obtained short
Phase power load forecasting module.
In the above-mentioned technical solutions, the constraint function of the principal component component are as follows:
s.t.WTW=I (6)
In formula (6), W is the principal component component data of short-term electric load, and X is to remove average data collection.
In the above-mentioned technical solutions, the supporting vector machine model are as follows:
F (x)=ω × φ (xi)+b (8)
In formula (8), in formula, ω × φ (x) is the inner product of higher dimensional space vector ω and Nonlinear Mapping φ (x), ω's
Dimension is higher dimensional space dimension, and b ∈ R is amount of bias.
In the above-mentioned technical solutions, the original optimization problem of the supporting vector machine model are as follows:
The constraint condition of formula (9) are as follows:
For formula (9) into (10), C is penalty coefficient, and the data sample that training error is more than ε is punished more in the bigger expression of C
Greatly, ξ and ξ*For slack variable, ε is insensitive loss function, the expression formula of ε are as follows:
In formula (11), f (x) indicates that the regression estimates function of support vector machines, y indicate prediction output valve.
In the above-mentioned technical solutions, the primal-dual optimization problem of the supporting vector machine model are as follows:
The constraint condition of formula (12) are as follows:
Formula (12) is into (13), αiWithBe Lagrange multiplier andxiFor supporting vector, b is
Threshold value.
In the above-mentioned technical solutions, the kernel function are as follows:
In formula (15), x is the center of kernel function；σ2For the form parameter of kernel function.
In the above-mentioned technical solutions, the Short-term Load Forecasting are as follows:
In formula (16), f (x) indicates the regression estimates function of support vector machines.
Above-mentioned technical proposal of the embodiment of the present invention is described in detail below in conjunction with application example:
As shown in Figure 1, in a kind of Short-Term Load Forecasting Method of the invention, comprising:
101, short-term electric load sample data is obtained from historical data, specifically:
1011, historical load data is obtained from historical data；
1012, by historical load data arrange for matrix size be m × k dimension sample matrix, the sample matrix be it is short
Phase electric load sample data.
The short-term electric load sample data are as follows:
102, it is analyzed, is obtained short-term using principal component analysis technology (PCA) for short-term electric load sample data
The principal component component data of electric load；Specifically:
1021, short-term electric load sample data is subjected to centralization, obtains average data collection；
The matrix of formula (1) is subjected to centralization:
Centralization is carried out for short-term electric load sample data, that is, makes the equal of short-term electric load sample data
Value is zero.
1022, the covariance matrix for removing average data collection is calculated；
1023, the characteristic value and corresponding feature vector of the covariance matrix are found out；
1024, the characteristic value of the covariance matrix is sorted from large to small, takes out maximum n characteristic value, the n is extremely
It is less 1；In the present embodiment by taking n=1 as an example；
1025, by feature vector composition characteristic matrix corresponding to n characteristic value；
1026, the constraint function of principal component component is constructed, and short-term electric load sample data is projected into eigenmatrix
In, obtain the principal component component data of short-term electric load.
Assuming that being { w by transformed coordinate system1；w2..., wd, wherein w is normal orthogonal base vector.If by data
After dimensionality reduction, characteristic xiZ is projected as in low-dimensional coordinate systemi=(zi1；zi2；…；zid′), it is based on ziTo construct xi, as a result are as follows:
So reconstructWith the x of scriptiDistance are as follows:
In order to reach dimensionality reduction effect, answer formula (5) minimum, due to ∑ xixi TCovariance matrix is represented, is calculated least
The constraint function of characteristic dimension is just are as follows:
s.t.WTW=I (6)
In formula (6), W is the principal component component data of short-term electric load, and X is to remove average data collection.
103, support vector machines (SVR) model is constructed, and training set is constructed according to principal component component data；
Principal component component data is tieed up by obtaining m n after step 102 dimensionality reduction, wherein n < k:
According to above-mentioned principal component component data, training set { (x is constructedi,yi), i=1,2 ..., m }, wherein xi∈Rn, yi∈
R, respectively input value and corresponding output valve, RnIt is respectively that real number space is tieed up in n peacekeeping 1 with R.
The supporting vector machine model are as follows:
F (x)=ω × φ (xi)+b (8)
In formula (8), ω × φ (x) is the inner product of higher dimensional space vector ω and Nonlinear Mapping φ (x), and the dimension of ω is
For higher dimensional space dimension, b ∈ R is amount of bias.
104, supporting vector machine model is trained with training set, obtains Short-term Load Forecasting, specifically
Ground:
1041, by Wolfe dual theorem combination method of Lagrange multipliers, the original optimization of supporting vector machine model is asked
Topic is converted into the primal-dual optimization problem of supporting vector machine model；
By slack variable ξ and ξ*It is introduced into formula (8), and solves ω, b and make entire solution space (including sample point),
Just obtain the original optimization problem of supporting vector machine model:
The constraint condition of formula (9) are as follows:
For formula (9) into (10), C is penalty coefficient, and the data sample that training error is more than ε is punished more in the bigger expression of C
Greatly, ξ and ξ*For slack variable, ε is insensitive loss function, the expression formula of ε are as follows:
In formula (11), f (x) indicates that the regression estimates function of support vector machines, y indicate prediction output valve.
Since above-mentioned original optimization problem belongs to the convex quadratic problem of high-dimensional feature space, any symmetric function is introduced
K(xi,xj), and it is made to meet Mercer theorem, to replace Nonlinear Mapping φ (x) as kernel function.Using Wolfe antithesis
Theorem simultaneously combines method of Lagrange multipliers, converts primal-dual optimization problem for the problem；
The primal-dual optimization problem of the supporting vector machine model are as follows:
The constraint condition of formula (12) are as follows:
Formula (12) is into (13), αiWithBe Lagrange multiplier andxiFor supporting vector, b is
Threshold value.
1042, kernel function is introduced, and is solved with primal-dual optimization problem of the training set to supporting vector machine model, is obtained
To Short-term Load Forecasting.
With training set { (xi,yi), i=1,2 ..., m }, it is solved, can be obtained for the objective function of formula (11)
To the regression estimates function of support vector machines:
In formula (14), αiWithBe Lagrange multiplier andxiFor supporting vector, b is threshold value,
Regression function is just characterized by supporting vector completely.During solving above-mentioned primal-dual optimization problem, only need to determine parameter ε, C and
Kernel function K (xi, x), wherein ε and C is used to control VC (Vapnik-Chervonenkis) dimension of regression function.Kernel function K (xi,
X) Gaussian radial basis function (RBF) is selected, expression formula are as follows:
In formula (15), x is the center of kernel function；σ2For the form parameter of kernel function.
105, the following short-term electric load is predicted using the Short-term Load Forecasting；
The Short-term Load Forecasting are as follows:
The following short-term electric load is predicted with model described in formula (16).
In the present invention, the Short-term Load Forecasting based on SVR is a kind of effective load forecasting model, to go through
History load data constructs training sample, continually enters new load data and updates regression function, establish optimized parameter, improves prediction
Speed.But with the increase of number of samples, required calculating time and space storage resource can all increase in geometric progression, cause
Arithmetic speed decline.Therefore, it is led to the problem of SVR, the present invention pre-processes data sample with PCA, eliminates number
According to correlation and noise, extract include sample data information pivot, reduce the dimension of sample space, greatly simplify calculating and
Space is saved, SVR arithmetic speed is improved.It follows that the present invention can carry out future electrical energy load accurately, in real time, reliably
Prediction.
The embodiment of the present invention is described with above attached drawing, but the invention is not limited to above-mentioned specific
Embodiment, the above mentioned embodiment is only schematical, rather than restrictive, those skilled in the art
Under the inspiration of the present invention, without breaking away from the scope protected by the purposes and claims of the present invention, it can also make very much
Form, all of these belong to the protection of the present invention.
Claims (10)
1. a kind of Short-Term Load Forecasting Method characterized by comprising
Short-term electric load sample data is obtained from historical data；
Analyzed for short-term electric load sample data using principal component analysis technology, obtain short-term electric load it is main at
Divide component data；
Supporting vector machine model is constructed, and training set is constructed according to principal component component data；
Supporting vector machine model is trained with training set, obtains Short-term Load Forecasting；
The following short-term electric load is predicted using the Short-term Load Forecasting.
2. Short-Term Load Forecasting Method according to claim 1, which is characterized in that described to be obtained from historical data
Short-term electric load sample data, specifically includes:
Historical load data is obtained from historical data；
By historical load data arrange for matrix size be m × k dimension sample matrix, the sample matrix be short-term electric load
Sample data.
3. Short-Term Load Forecasting Method according to claim 1, which is characterized in that described to be directed to short-term electric load
Sample data is analyzed using principal component analysis technology, is obtained the principal component component data of short-term electric load, is specifically included:
Short-term electric load sample data is subjected to centralization, obtains average data collection；
Calculate the covariance matrix for removing average data collection；
Find out the characteristic value and corresponding feature vector of the covariance matrix；
The characteristic value of the covariance matrix is sorted from large to small, maximum n characteristic value is taken out, the n is at least 1；
By feature vector composition characteristic matrix corresponding to n characteristic value；
The constraint function of principal component component is constructed, and short-term electric load sample data is projected in eigenmatrix, is obtained short
The principal component component data of phase electric load.
4. Short-Term Load Forecasting Method according to claim 3, which is characterized in that described to use training set to support
Vector machine model is trained, and obtains Short-term Load Forecasting, is specifically included:
By Wolfe dual theorem combination method of Lagrange multipliers, convert the original optimization problem of supporting vector machine model to
The primal-dual optimization problem of supporting vector machine model；
Kernel function is introduced, and is solved with primal-dual optimization problem of the training set to supporting vector machine model, short-term electricity is obtained
Power load forecasting model.
5. Short-Term Load Forecasting Method according to claim 3, which is characterized in that the constraint of the principal component component
Function are as follows:
s.t.WTW=I (6)
In formula (6), W is the principal component component data of short-term electric load, and X is to remove average data collection.
6. Short-Term Load Forecasting Method according to claim 4, which is characterized in that the supporting vector machine model
Are as follows:
F (x)=ω × φ (xi)+b (8)
In formula (8), in formula, ω × φ (x) is the inner product of higher dimensional space vector ω and Nonlinear Mapping φ (x), the dimension of ω
As higher dimensional space dimension, b ∈ R are amount of bias.
7. Short-Term Load Forecasting Method according to claim 6, which is characterized in that the supporting vector machine model
Original optimization problem are as follows:
The constraint condition of formula (9) are as follows:
For formula (9) into (10), C is penalty coefficient, and the bigger expression of C punishes bigger, ξ to the data sample that training error is more than ε
And ξ*For slack variable, ε is insensitive loss function, the expression formula of ε are as follows:
In formula (11), f (x) indicates that the regression estimates function of support vector machines, y indicate prediction output valve.
8. Short-Term Load Forecasting Method according to claim 6, which is characterized in that the supporting vector machine model
Primal-dual optimization problem are as follows:
The constraint condition of formula (12) are as follows:
Formula (12) is into (13), αiWithBe Lagrange multiplier andxiFor supporting vector, b is threshold value.
9. Short-Term Load Forecasting Method according to claim 8, which is characterized in that the kernel function are as follows:
In formula (15), x is the center of kernel function；σ2For the form parameter of kernel function.
10. Short-Term Load Forecasting Method according to claim 9, which is characterized in that the short-term electric load is pre-
Survey model are as follows:
In formula (16), f (x) indicates the regression estimates function of support vector machines.
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| CN112365280B (en) * | 2020-10-20 | 2024-04-19 | 国网冀北电力有限公司计量中心 | Electric power demand prediction method and device |
| CN112613221A (en) * | 2020-12-28 | 2021-04-06 | 广州大学城能源发展有限公司 | Client power load monitoring system |
| CN113065471A (en) * | 2021-04-02 | 2021-07-02 | 合肥工业大学 | Short-term load prediction method of power system |
| CN113065471B (en) * | 2021-04-02 | 2022-08-30 | 合肥工业大学 | Short-term load prediction method of power system |
| CN113011680A (en) * | 2021-04-16 | 2021-06-22 | 西安建筑科技大学 | Power load prediction method and system |
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